The line shown in the xy-plane in the graph of y = f(x). For what value of x is f(x) = f^(-1) (x)? A) -8 B) -6 C) -4 D) 10

Q: Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from…

A: The line passes through the point (6,7) that cuts off the least area from the first quadrant.

Q: What are the coordinates of the points in the graph of y² –x²+ 6x – 13=0 in which the tangent line…

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Q: Find the slope of the line tagent to the curve of y = In x/x at point (1,0)

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Q: How is linear approximation used to approximate the value of afunction ƒ near a point at which ƒ and…

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Q: y = vx² – 9

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Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (-1,…

A: Given that f(x)=x2 To find two tangents that passes through (-1,-3)

Q: Please show step-by-step solution!

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Q: Find equations of the two tangent lines to the graph of f(x) = 2x2 that pass through the point (-1,…

A: Here, the given curve is: f(x)=2x2 To find two tangent lines that pass through (-1,-6)

Q: Find equations of the two tangent lines to the graph of f(x) = x² that pass through the point (1,…

A:

Q: The tangent line equation of 2x6+y4=9xy at the point (1, 2) is ... ....E Persamaan garis singung…

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Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A: Topic - tangent lines to curve passing through Given point outside curve

Q: What is the maximum vertical distance between the line y =x +2and the parabola y =x2 for     -1 ≤ x…

A:

Q: The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent…

A: Given that the curve passes through a point.

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: the tangent line to the graph (x^2 + 4)y = 8 at the point (2, 1).

A: Use formula of  equation of tangent  line

Q: The slope of the tangent line to the graph of the function y = 9/ – 2 at (4, 16) is - -5.00 2.25…

A: To find the slope of the tangent line for the given function at (4,16)

Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

A:

Q: 9) Write an equation of the tangent line to the graph of y = 5x2 - 8 at the point where x 0. %3D -3x…

A: Quotient rule of derivative of the function f(x)=u(x)/v(x) is

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – axis…

A: Solution

Q: Find an equation of the tangent line to the curve y = 2x2 +3 that is parallel to the line 82 – y + 3…

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Q: The slope of the tangent line to the curve y 4 at the point (4, 1) is: - The equation of this…

A: The slope of tangent to any curve is determined by the derivative . So, slope of the tangent…

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

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Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: Find the slope and y-intercept of the line through the point (6,6) that cuts off the least area from…

A: Given : Point (6,6)

Q: Compute the slope of the secant line containing the points (1, f (1)) and D) on the graph of f (x) =…

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Q: Find the equation of the tangent line of funclion y= ²+1 23 -2 at (40,- 73)

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Q: A few years ago, there were light sabre battles. What is the distance between two light sabers given…

A: Solution of this question is

Q: How many tangent lines to the curve y = x/(x + 1) pass through the point (1, 2)? At which points do…

A: The tangent lines to the curve y=xx+1 passes through the point (1, 2)

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

A:

Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

Q: Find the equation of the tangent line to the function f(x) 8vx - 4 at the point (64, 60). Provide…

A: Calculate the slope of the given function;

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x – 3x and…

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Q: Find the slope of the tangent line to the graph of x4 + 5xy - 12x + 11 = dt at the point (1 , 0) on…

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Q: Determine the equation of the line tangent to the curve square root(xy)=x-2y  at point (4,1)

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Q: Find the slope of the tangent line of f (x) = 2x² - 3x + 2 at x = 2 %3D

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Q: What are the coordinates of the points in the graph of y? - - x2 + 6x – 13 = 0 in which the tangent…

A: Note that the slope of a horizontal line is zero. Also the slope of a tangent is given by the…

Q: Find equations of the two tangent lines to the graph of f(x) = x2 that pass through the point (-1,…

A:

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: Find the point on the parabola y= X- + 4 whose tangent line is parallel with y = 3x -5

A: Let a point on the parabola is h,k. Now the slope of the tangent line is given by: m=dydxh,k Since,…

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Q: From the point (2,2), find the directions in which the directional derivative of f(x,y)=x2 +xy3…

A: Given f(x, y)=x2+xy3 we have to find the directions in which the directional derivative of function…

Q: Find the x-coordinates of all points on the curve y = 12x" - 96x° - 168x + 26x + 91 where the…

A:

Q: What is the equation of the curve that passes through the point (0, 3) and has a slope at any point…

A: We have to find

Q: Determine the line tangent to f(x) = 2x2 + 3x + 1 at (-2, 3).

A: The tangent line to a curve at a given point is the line which intersects the curve at the point and…

Q: What is the slope of the curve y= 2 over √x at the point (4,1)

A: To find the slope at a particular point x=a, the first derivative of the function is taken. Once the…

Q: What are the coordinates of the point on the graph of Ax) = (x+ 1)(x+ 2) at which the tangent is…

A: solution:-f(x)=x+1x+2      =x2+3x+2slope of tangent=ddxf(x)                             =ddxx2+3x+2…

Q: Find the slope and y-intercept of the line through the point (1,2) that cuts off the least area from…

A: Given : Point ( 1 , 2 )  It cuts off the least area from the first  quadrant

Q: Find the equation of the tangent line to the function f(x) = 8/x - 2 at the point (64, 62). Provide…

A: To determine the equation of the tangent in the form y =mx+b

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.